弱Orlicz鞅空间的弱原子分解及其应用

Weak Atomic Decompositions of Weak Orlicz Martingale Spaces and Applications

对3类由凹函数生成的弱Orlicz鞅空间建立了相应的弱原子分解.作为应用,首先给出了这些弱Orlicz鞅空间上次线性算子有界的一个充分条件,并在此基础上证明了一些弱型鞅不等式,然后证明了关于这些弱Orlicz鞅空间的Marcinkiewicz型插值定理.

In this paper,weak atomic decompositions of three kinds of weak Orlicz martingale spaces generated by concave functions are established.As applications,the author first gives a sufficient condition for a sublinear operator to be bounded on weak Orlicz martingale spaces,and based on this,some weak-type martingale inequalities are proved.Then,the author proves a Marcinkiewicz-type interpolation theorem for weak Orlicz martingale spaces.